(a) Field of the Invention
The present invention relates to a positive feedback RC active biquadratic filter circuit.
(b) Description of Prior Art
In the design of active filters, it is often desirable to construct a filter in common sections which can easily be manufactured in series. These sections are often referred to as sub-networks and they are required to be sufficiently versatile whereby filter circuits may be constructed using the individual sections whereby to obtain a large spectrum of desired filter characteristics. Generally, these sub-networks are of the second order and connected in cascade or otherwise. These sections render a transfer function of the biquadratic type and which can be expressed mathematically, as is well known, by the equation: ##EQU1##
A large number of circuit configurations are known in the art, such as gyrator, generalized immittance converter, biquad-loop, single amplifier biquad, which circuit configurations can realize the transfer function mathematically expressed above. By comparing the calculations of the sensitivity of such sub-networks, it is seen that the single amplifier biquad sub-network will give a better performance. A popular one of such single amplifier biquad is that described in U.S. Pat. No. 3,919,658 issued on Nov. 11, 1975 to J. J. Friend and assigned to Bell Telephone Laboratories Incorporated. This patent describes a biquad filter using a single operational amplifier with negative feedback. Reference is also made to an article by G. Wilson et al entitled "RC-Active Networks with Reduced Sensitivity to Amplifier Gain-Bandwidth Product", IEEE Trans-on Circuits Syst, vol. CAS-21, No. 5, Sept. 1974, pp. 618-626. This article deals with single amplifier biquad networks and suggests band-pass or band-stop resonator applications. Reference is also made to an article by P. E. Fleisher, entitled "Sensitivity Minimization in a Single Amplifier Biquad Circuit", IEEE Trans. Circuits Syst., vol. CAS-23, Jan. 1976, pp. 45-55. In this article, Fleisher deals with the single amplifier biquad of Friend for a band-pass application. For configurations in applications of Low-Pass Notch, and High-Pass Notch, it is noted that the poles and the zeros cannot be too far apart in order to maintain approximately the same optimal topology that is obtained with band-pass resonators. However, when we realize an elliptical low-pass filter at high frequency, the disadvantages become more pronounced.
Another factor to be considered, is that in the technology of silicium, seeing that the thermal coefficient of the elements used in the active operational amplifiers is relatively large (of the order of a few thousand ppm/.degree.C.), the active RC filter must be of a quality which is insensitive to the product of "gain-bandwidth" in the operational amplifier utilized. Consequently, the active RC filters are of the low frequency type. The present state of the art is that the operational amplifier utilized 0.1 to 0.2% of the gain-bandwith and this is for the good configurations of active RC filters realized with operational amplifiers with internal compensation (first order).